Flow batteries are electrochemical energy storage systems in which electrochemical reactants, typically redox active compounds, are dissolved in liquid electrolytes, which are individually contained in negative electrolyte and positive electrolyte loops and circulated through reaction electrochemical cells where electrical energy is either converted to or extracted from chemical potential energy in the reactants by way of reduction and oxidation reactions. Especially in larger systems, which may comprise multiple electrochemical cells or stacks, it is important to be able to monitor the state-of-charge of each of the electrolytes, for example to know when the flow battery is “full” or “empty” before actually realizing these end states.
The state of charge (SOC) of the electrolyte expresses the ratio of concentrations of charged to uncharged active material and is a useful parameter for describing what fraction of a battery's capacity is utilized storing energy. If all the active material is discharged, the electrolyte is said to have a state of charge of 0%, and if all the active material is in the charged state, the state of charge is 100%. At any intermediate state of charge (0%<SOC<100%) there will be a non-zero concentration of both charged active material and discharged active material.
For optimal performance, the initial state of such a system typically provides that the negative electrolyte and positive electrolyte contain equimolar quantities of the redox active species. But after the system has experienced some number of charge/discharge cycles, the positive electrolyte and negative electrolyte may become imbalanced because of side reactions during these operations—for example, in some aqueous systems generation of hydrogen from water causes the negative electrolyte to achieve a lower state of charge than the positive electrolyte.
An imbalanced state may be corrected by processing the electrolyte in a rebalancing cell. Before this can be done, however, it is necessary to assess the state-of-charge of the individual electrolytes to determine how much of the rebalancing reaction is required to rebalance the system.
State-of-charge monitoring for flow battery electrolytes can be done using electrochemical measurements. Electrochemical measurements typically measure the equilibrium half-cell potential by comparing the solid potential of an electrode, such as a platinum electrode, that is submersed in the electrolyte solution with the potential of a reference electrode of known and fixed potential in ionic contact with the solution. For any composition of charged and uncharged active materials (0%<SOC<100%) there is a unique value of the equilibrium half-cell potential, Eeq, given by the Nernst equation (Eq. 1)
                              E          eq                =                              E            0                    -                                    RT                              n                ⁢                                                                  ⁢                F                                      ⁢                          ln              ⁡                              (                                                      c                    R                                                        c                    O                                                  )                                                                        (        1        )            where Eo is the standard potential of the redox couple, R is the gas constant, T is the temperature of the electrolyte, n is the number of electrons involved in the reaction, F is Faraday's constant, cR is the concentration of reduced species and cO is the concentration of oxidized species. Equation 2 shows eq 1 in terms of percent of reduced species, S.
                              E          eq                =                              E            0                    -                                    RT                              n                ⁢                                                                  ⁢                F                                      ⁢                          ln              ⁡                              (                                  S                                      100                    -                    S                                                  )                                                                        (        2        )            
Rearranging equations 2 to solve for S yields eq 3.
                    S        =                  (                      100                          1              +                              1                                  exp                  ⁡                                      [                                                                  -                                                                              n                            ⁢                                                                                                                  ⁢                            F                                                    RT                                                                    ⁢                                              (                                                                              E                            eq                                                    -                                                      E                            0                                                                          )                                                              ]                                                                                )                                    (        3        )            
The typical method for determining the state of charge of a solution is to measure the equilibrium half-cell potential by comparing the solid potential of the electrode to a calibrated reference electrode and calculate S using equations 3. It is, however, often difficult to obtain accurate measurements of the solid potential because the reference electrodes against which the solid potential is measured are prone to potential drift and ‘fouling’ when in contact with electrolyte for extended periods.
The present disclosure provides, inter alia, improved methods for determination of state of charge and methods for balancing the state of charge using such methods.